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Popular >

derivative of (3x-2^2(2x+1)^4)

Solution

\frac{d}{d x} ((3 x - 2)^{2} (2 x + 1)^{4})

Solution

6 (3 x - 2) (2 x + 1)^{4} + 8 (2 x + 1)^{3} (3 x - 2)^{2}

Solution steps

\frac{d}{d x} ((3 x - 2)^{2} (2 x + 1)^{4})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (3 x - 2)^{2}, g = (2 x + 1)^{4}

= \frac{d}{d x} ((3 x - 2)^{2}) (2 x + 1)^{4} + \frac{d}{d x} ((2 x + 1)^{4}) (3 x - 2)^{2}

\frac{d}{d x} ((3 x - 2)^{2}) = 6 (3 x - 2)

\frac{d}{d x} ((2 x + 1)^{4}) = 8 (2 x + 1)^{3}

= 6 (3 x - 2) (2 x + 1)^{4} + 8 (2 x + 1)^{3} (3 x - 2)^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of (3x-2^2(2x+1)^4) ?
The derivative of (3x-2^2(2x+1)^4) is 6(3x-2)(2x+1)^4+8(2x+1)^3(3x-2)^2
What is the first derivative of (3x-2^2(2x+1)^4) ?
The first derivative of (3x-2^2(2x+1)^4) is 6(3x-2)(2x+1)^4+8(2x+1)^3(3x-2)^2